Ergodic BSDE with an unbounded and multiplicative underlying diffusion and application to large time behavior of viscosity solution of HJB equation

In [21, 23] the authors have discussed the existence and uniqueness of a weak solution and have also proved the linear stability around the nontrivial steady state of the

In this article we study the large-time behavior of the solution to a general Rosenau type approximation to the heat equation [16], by showing that the solution to this

On the other hand, we show that if the potential is an isotropic harmonic potential with a time dependent frequency which decays sufficiently fast, then Sobolev norms are bounded,

In the case of isothermal models γ = 1, we showed that, by choosing the scaling τ as solution to an appropriate differential equation (which can be inferred via a parallel

(3) As a consequence of these assumptions, the solutions of (1)-(2) are Lipschitz continuous and periodic in x and, in good cases, they are expected to remain uniformly bounded in x

Nonlinear degenerate parabolic equations, Nonlinear degenerate elliptic equations, Hamilton-Jacobi equations, monotone systems, gradient bounds, oscillation, strong maximum

We study the high frequency limit for the dissipative Helmholtz equation when the source term concentrates on a submanifold of R n.. We prove that the solution has a

In contrast to the small size behavior which is dominated by the properties of the daughter distribution function b, the behavior of f for large sizes is determined by the